一类均匀拟阵的二阶圈图连通性及哈密顿性

doi:10.6040/j.issn.1671-9352.0.2020.398

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (5): 92-96.doi: 10.6040/j.issn.1671-9352.0.2020.398

• • 上一篇

一类均匀拟阵的二阶圈图连通性及哈密顿性

邓梓健¹,刘彬¹,火博丰^1,2*

1.青海师范大学数学与统计学院, 西宁青海 810008;2.青海省物联网重点实验室, 西宁青海 810008

发布日期:2022-05-27
作者简介:邓梓健(1996— ), 男, 硕士研究生, 研究方向运筹学与控制论、图论与组合优化. E-mail:1329205716@qq.com*通信作者简介:火博丰(1967— ), 女, 博士, 教授, 研究方向运筹学与控制论、图论与组合优化. E-mail:124356595@qq.com
基金资助:
国家自然科学基金资助项目(11961055,11801296);青海省科技厅资助项目(2018-Z-718)

Connectivity and Hamiltonian properties of second order circuit graphs of a class of uniform matroid

DENG Zi-Jian¹, LIU Bin¹, HUO Bo-feng^1,2*

1. College of Mathematics and Statistics, Qinghai Normal University, Xining 810008, Qinghai, China;
2. Internet of Things Key Laboratory, Xining 810008, Qinghai, China

Published:2022-05-27

摘要/Abstract

摘要： 对均匀拟阵U2,n的二阶圈图的连通性及哈密顿性进行研究,得到了U2,n的二阶圈图是3(n-3)-正则图并给出相关证明, 而且得到其点连通度和边连通度都等于最小度的连通性质。介绍了U2,n的二阶圈图的哈密顿性,证明其是哈密顿连通的。

关键词: 均匀拟阵, 二阶圈图, 连通度, 最小度, 哈密顿连通

Abstract: The connectivity and Hamiltonian properties of the second order circuit graph of the uniform matroid U2,n have been investigated. The second order circuit graph of U2,n is 3(n-3)-regular graph and the connectivity and edge-connectivity of its are equal to the minimum degree. Furthermore, Hamiltonian properties of the second order circuit graph of U2,n is introduced and it is Hamiltonian connected.

Key words: uniform matroid, second order circuit graph, connectivity, minimum degree, Hamiltonian connected

中图分类号:

O157.5

邓梓健,刘彬,火博丰. 一类均匀拟阵的二阶圈图连通性及哈密顿性[J]. 《山东大学学报(理学版)》, 2022, 57(5): 92-96.

DENG Zi-Jian, LIU Bin, HUO Bo-feng. Connectivity and Hamiltonian properties of second order circuit graphs of a class of uniform matroid[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(5): 92-96.

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一类均匀拟阵的二阶圈图连通性及哈密顿性

Connectivity and Hamiltonian properties of second order circuit graphs of a class of uniform matroid

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